According to the police, expensive cigars and pink champagne flowed into the prime minister’s official Jerusalem residence in quantities sufficient to stock a small cocktail lounge. The generous patrons included Arnon Milchan, the Israeli movie producer.

But it is the favors Mr. Netanyahu may have given his wealthy friends in return that could herald his downfall. A formal bribery charge would be by far the most serious outcome, and the most ominous for his political survival.

Mr. Netanyahu is serving his third consecutive term since his election in 2009, and his fourth overall since the 1990s. If he remained in the post through July 2019, he would set a record for total time in office, surpassing that of the state’s founder, David Ben-Gurion.

Mr. Netanyahu has vehemently denied any wrongdoing and has vowed to fight on, saying that no police recommendation would prompt his resignation.

His longevity attests to his political agility and to his perfection of a campaigning and governing style in which he casts his political foes and critics as enemies of the broader body politic. Though he has formed previous ruling coalitions with those to his left, his current government is often described as the most right-wing and religious in Israel’s history.

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Arnon Mozes, publisher of the popular daily Yediot Aharonot, last year.Credit Reuters

But while Mr. Netanyahu has prepared the public for this moment for months, and made strenuous efforts to discredit those investigating him, he has not prepared Israel or his government for the possibility that he may be unable to continue to lead. He has designated no successor, and no single member of his own coalition has emerged as ready to step into his shoes. Meanwhile, a centrist opposition, led by Yair Lapid of the Yesh Atid party, has been gaining strength.

The Israeli law enforcement authorities have handled the cases with great caution, wary of the possibility of bringing down a prime minister who might then be proved not guilty in court, not least with Israel facing increasing security threats on its northern and southern frontiers.

But Israel’s constant state of alert has led some critics to argue all the more that a prime minister so focused on fighting his own legal battles cannot be entrusted with fateful decisions of peace and war.

Mr. Netanyahu long ago earned the nickname “the Magician” for his uncanny knack for political endurance, and even his most ardent opponents have been hesitant to write him off.

At what point Mr. Netanyahu might be legally required to step down, short of a final conviction, is likely to be a matter of increasingly heated debate, though public opinion and political pressure could in the end play a decisive role.

Israel’s Supreme Court has ruled in the past that government ministers or deputy ministers, once indicted, may not remain in their posts. Whether that principle should also apply to the elected prime minister is an open question.

Mr. Netanyahu would be something of a test case as Israel’s first sitting prime minister to be formally charged.

His predecessor, Ehud Olmert, announced his resignation in September 2008, a week after the police recommended he be charged with bribery, breach of trust, money laundering and fraudulent receipt of goods. That case involved an American businessman and a travel-expense scandal from Mr. Olmert’s days as mayor of Jerusalem and minister of industry and trade.

Mr. Olmert was eventually convicted in various cases and served 19 months of a 27-month prison sentence. He was released last year.

Pre-empting the police recommendations, Mr. Netanyahu told the public to expect them and did his best to minimize their importance.

“Any fair-minded person will ask themselves how people who say such delusional things about the prime minister can investigate him objectively and make recommendations in his case without bias,” he wrote on a Facebook post last week, accusing the police commissioner, Roni Alsheich, of having an agenda.

In December, Mr. Netanyahu told a gathering of his right-wing Likud Party supporters in December: “The vast majority of police recommendations end in nothing. Over 60 percent of the police recommendations are thrown in the trash. Over 60 percent of the police recommendations don’t get to an indictment.”

Experts have disputed those figures, however, and the prime minister’s opponents have begun quoting from an interview he gave in 2008, at the height of Mr. Olmert’s legal troubles, to turn the tables on Mr. Netanyahu.

Describing Mr. Olmert as “up to his neck in investigations,” Mr. Netanyahu said of his political rival at the time: “He does not have a public or moral mandate to determine such fateful matters for the state of Israel when there is the fear, and I have to say it is real and not without basis, that he will make decisions based on his personal interest in political survival and not based on the national interest.”

In some ways, though, Mr. Netanyahu has been here before.

During his first term in office, in the late 1990s, the police recommended that he be charged with fraud and breach of trust in a complicated case in which Mr. Netanyahu was suspected of acting to appoint an attorney general who would be sympathetic to a minister under investigation for corruption, in return for that minister’s political support. Ultimately, the attorney general closed that case, citing a lack of evidence.

Again, in March 2000, once Mr. Netanyahu was out of office, the police recommended that he be charged with bribery, fraud and breach of trust in a case involving his holding on to $100,000 in gifts that were state property and having the state pay for private work on his home. Months later, the attorney general also ordered that case closed.

This time around, the police recruited a state’s witness, Ari Harow, Mr. Netanyahu’s former chief of staff and once one of his closest confidants.

The police have also been making headway in other criminal investigations in which Mr. Netanyahu has not been named as a subject, but that involve associates from his most inner circle.

One scandal, called Case 3000, involves a $2 billion deal for the purchase of submarines and missile ships from a German supplier. Critics have described that episode as potentially the biggest corruption case in Israeli history, touching on deep conflicts of interest and national security.

Among those caught up in the shipping investigation are David Shimron, Mr. Netanyahu’s personal lawyer and second cousin, and Yitzhak Molcho, Mr. Netanyahu’s lifelong friend and close adviser, whom he has sent on his most delicate diplomatic missions since the 1990s. Mr. Molcho and Mr. Shimron are partners in a law firm as well as brothers-in-law.